Bella is her name, meaning “beauty” in Italian. She’s a main character in Twilight and gets most of the pages and screen time in the movie because the story is told from her point of view.
Everyone knows the story of Beauty and the Beast and how she tames the beast through love. Isn’t that pretty much the story of Twilight? That’s not to say the book/movie adaptation is derivative—far from it. For the beast, in this case, is a vampire and has enemies. Of course, the original beast is also hated for being, well, a beast. But a vampire is indeed evil for killing people. Wow! What a guy to come across.
In the Disney animated version of B&B Belle (French for beautiful, or Bella in Italian) is a feisty and very brave young woman. She positively seeks out the Beast and stands up to him whilst beginning to fall in love. She has agency and grit. She is a willing substitute for her imprisoned father and does it out of her love for him.
Conversely, Bella in the movie, at least, is somewhat passive. Yes, she is attracted to Edward, a Heathcliff-like brooding presence in her life, enigmatic and not a little frightening. Yes, she overcomes his reluctance to engage with her, and they form a relationship. But we learn he is obsessed with her because he can’t read her thoughts as he can with others around him. As such, this special quality she has is the driver for his willingness to be with her. So how much is Bella’s doing to see through the bestial to the kind inner person? It’s not particularly clear.
Despite his obsession, he also considers that they shouldn’t form a relationship. And one can see why. He’s centuries old and lives a strange predatory life, though he is, by the time of the story, an “ethical vampire” and doesn’t drain people’s blood, despite the desire to do so. So a great mismatch between a teen who is stepping out in life and this aged and experienced individual. It’s a bit of a cliché: the younger woman attracted to the older, successful man. Yet at one level that is what this story is about.
Twilight differs considerably from the original fairy tale. There’s no beast dying because Belle left him. There are no siblings and the father isn’t destitute or gets lost and taken prisoner or put under any obligation to hand over his daughter. So, as a story, Twilight deviates considerably from B&B. That said, at it’s core is the man-woman or even husband-wife relationship with the woman seeking a suitable partner (a super-strong vampire fits the bill!).